Journal of the Korea Institute of Information Security & Cryptology (정보보호학회논문지)

Korea Institute of Information Security and Cryptology (한국정보보호학회)
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A Flexible Approach for Efficient Elliptic Curve Multi-Scalar Multiplication on Resource-constrained Devices

자원이 제약된 장치에서 효율적인 타원곡선 다중 상수배의 구현을 위한 유연한 접근

  • Seo, Seog-Chung (Gwangju Institute of Science and Technology Department of information and Communications) ;
  • Kim, Hyung-Chan (Gwangju Institute of Science and Technology Department of information and Communications) ;
  • Ramakrishna, R.S. (Gwangju Institute of Science and Technology Department of information and Communications)
  • 서석충 (광주과학기술원 정보통신공학과) ;
  • 김형찬 (광주과학기술원 정보통신공학과) ;
  • 라마크리시나 (광주과학기술원 정보통신공학과)
  • Published : 2006.12.31
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Abstract

Elliptic Curve Cryptosystem (ECC) is suitable for resource-constrained devices such as smartcards, and sensor motes because of its short key size. This paper presents an efficient multi-scalar multiplication algorithm which is the main component of the verification procedure in Elliptic Curve Digital Signature Algorithm (ECDSA). The proposed algorithm can make use of a precomputed table of variable size and provides an optimal efficiency for that precomputed table. Furthermore, the given scalar is receded on-the-fly so that it can be merged with the main multiplication procedure. This can achieve more savings on memory than other receding algorithms. Through experiments, we have found that the optimal sizes of precomputed tables are 7 and 15 when uP+vQ is computed for u, v of 163 bits and 233 bits integers. This is shown by comparing the computation time taken by the proposed algorithm and other existing algorithms.

타원곡선 암호시스템은 작은 키 길이로 인하여 스마트카드, 센서 모트와 같은 메모리, 계산 능력이 제약된 장치에서 사용하기에 적합하다. 본 논문에서는 이러한 장치에서 타원곡선 서명 알고리즘 검증 (uP+vQ, u, v: 상수, P, Q: 타원곡선 위의 점)의 주된 계산인 다중 상수배를 효율적으로 계산하기 위한 알고리즘을 제안한다. 제안 알고리즘은 부분 윈도우와 Interleave 방법에 기반을 둔 것으로서 어떠한 크기의 사전계산 테이블이라도 이용할 수 있을 뿐만 아니라, 해당 테이블에서 최적의 nonzero 밀도를 제공한다. 또한 상수 리코딩이 테이블 조회를 사용하지 않고 상수배 계산과 함께 진행되기 때문에 기존의 다른 알고리즘에 비하여 더욱 메모리를 절약할 수 있다. 실험을 통하여 163비트의 u, v와, 233 비트의 u, v에 대하여 uP+vQ를 수행하는 데 필요한 계산량을 사전계산 테이블의 크기에 따라 비교함으로써 최적의 테이블 크기는 각각 7, 15임을 알아낼 수 있었다.

Keywords

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